The Midas Formula

Here's a short documentary to end the weekend; chronicling the discovery and use of the Black-Scholes model from its infancy to LTCM's collapse, this BBC production sheds some light into the minds of the academics who pursued it, the traders who loathed and then praised them, and how it changed the way options are being traded ever since.

The first few parts are a bit dragging though, somewhat over-dramaticized, and the narrator made me sleepy but all in all its pretty good stuff.

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Meanwhile in his letter to investors Buffet calls the Black-Scholes formula silly and points to the fact that he made money options trading through the crisis.

Meanwhile in this comment I call Warren Buffett silly and point out to him being a hypocrite who just talks his own book.

People like Coldplay and voted for the Nazis, you can't trust people Jeremy

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If I had asked people what they wanted, they would have said faster horses - Henry Ford

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The Black Scholes formula is a model for pricing only, just like DCF. As with any model/theory, the assumptions are everything. Often, the assumptions (or the market's inputs as far as assumptions) are wrong, so you can find many different ways to profit if you understand the model. I love options, so useful. :)

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If I had asked people what they wanted, they would have said faster horses - Henry Ford

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Unfortunately, I'm not convinced. After spending one year in an Econ PhD program, I suspect most economists like to see themselves as scientists, who seem to think that economics can be as precise, scientific, and quantitative (or is it quantifiable, I'm not really sure, I'm honestly drunk) as "real" sciences (like physics). They should really read Hayek's "The Prentense of Knowledge"...

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Econ, you misunderstand. There may be things that are not precise in economics, but I don't take it as writ that we can't strive to get there. It's not like the speed of light, there's no definite proof that we can't reach it.

For example, I'm willing to be there are 100s of dudes right now trying to square away black swans into the B-S theory. And that's a beautiful thing.

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Econ, you misunderstand. There may be things that are not precise in economics, but I don't take it as writ that we can't strive to get there. It's not like the speed of light, there's no definite proof that we can't reach it.

I suspect we can't get there. Seriously, read and understand F.A. Hayek's Noble Prize Speech/Lecture. I'm not saying you have to agree with him... I just think he lays out the arguments pretty well...

monkeysama:

For example, I'm willing to be there are 100s of dudes right now trying to square away black swans into the B-S theory. And that's a beautiful thing.

I'm not 100& sure what you're saying. Please explain (and, for some strange reason, I honestly think I agree with you on this point, even though I'm not even sure yet what you're saying...).

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Econ, you misunderstand. There may be things that are not precise in economics, but I don't take it as writ that we can't strive to get there. It's not like the speed of light, there's no definite proof that we can't reach it.

I suspect we can't get there. Seriously, read and understand F.A. Hayek's Noble Prize Speech/Lecture. I'm not saying you have to agree with him... I just think he lays out the arguments pretty well...

monkeysama:

For example, I'm willing to be there are 100s of dudes right now trying to square away black swans into the B-S theory. And that's a beautiful thing.

I'm not 100& sure what you're saying. Please explain (and, for some strange reason, I honestly think I agree with you on this point, even though I'm not even sure yet what you're saying...).

The main problem with B-S theory is that it doesn't take into account risk in a way that is satisfying - only volatility.When the twin snakes of the Asian financial crisis and the Russian default occurred the price to hedge risk by buying options spiked and it tanked LTCM. We now understand from the latest crisis that market failures and rallies, "black swans", are much more likely than a normal probability distribution would suggest (a so called fat tail distribution is a better fit). LTCM was not taking this into account and were using past data to justify much of their buying.

The newest challenge is to somehow account for the risk associated with black swans without sacrificing too much in terms of short term gains. I think that there is a new equation waiting to be found that will square option pricing with this new interpretation of risk.

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The main problem with B-S theory is that it doesn't take into account risk in a way that is satisfying - only volatility.

When the twin snakes of the Asian financial crisis and the Russian default occurred the price to hedge risk by buying options spiked and it tanked LTCM. We now understand from the latest crisis that market failures and rallies, "black swans", are much more likely than a normal probability distribution would suggest (a so called fat tail distribution is a better fit). LTCM was not taking this into account and were using past data to justify much of their buying.

The newest challenge is to somehow account for the risk associated with black swans without sacrificing too much in terms of short term gains. I think that there is a new equation waiting to be found that will square option pricing with this new interpretation of risk.

B-S equals Black-Scholes and not Black-Swan, right? I just want to make sure I know what you're saying...

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Then, what is a better way to take in risk? As far as I can tell, economists (and/or financial economists) don't have a good way to take into account risk (since nobody knows exactly what risk is). Is it undiversifiable risk? If so, how exactly do you quantify that?

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Then, what is a better way to take in risk? As far as I can tell, economists (and/or financial economists) don't have a good way to take into account risk (since nobody knows exactly what risk is). Is it undiversifiable risk? If so, how exactly do you quantify that?

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Then, what is a better way to take in risk? As far as I can tell, economists (and/or financial economists) don't have a good way to take into account risk (since nobody knows exactly what risk is). Is it undiversifiable risk? If so, how exactly do you quantify that?

That, my friend, is the billion dollar question.

Risk is a concept that means different things to different people. It is impossible to fully quantify.

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Then, what is a better way to take in risk? As far as I can tell, economists (and/or financial economists) don't have a good way to take into account risk (since nobody knows exactly what risk is). Is it undiversifiable risk? If so, how exactly do you quantify that?

That, my friend, is the billion dollar question.

Risk is a concept that means different things to different people. It is impossible to fully quantify.

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uh false dynamic hedging isn't some amazing way to reduce all your risk and just make a risk free return. It's a way to reduce your exposure to directional movements to focus on movements in volatility. these fuckers started LTCM to use their models to gain an edge on the market. If you are looking for a risk free return buy some treasures

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This is probably a dumb question, but so what if they priced in the fat tailed distribution? Wouldn't that just lower the amount of capital they were willing to risk? If so, wouldn't that also impede the return they could achieve in the absence of left tail events?

I guess what I'm trying to get at is, what exactly would have gone differently? They might have lost less money in 1998, but would it have been a whole lot less?

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This is probably a dumb question, but so what if they priced in the fat tailed distribution? Wouldn't that just lower the amount of capital they were willing to risk? If so, wouldn't that also impede the return they could achieve in the absence of left tail events?

I guess what I'm trying to get at is, what exactly would have gone differently? They might have lost less money in 1998, but would it have been a whole lot less?

You want a system that dynamically tells you the amount of left tailedness in the market at any time, real time. That's the holy grail.

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If someone could make a formula like B-S incorporating the fat tail risks that would be awesome!

Btw, if LTCM could get enough liquidity during the crisis, at some point the prices would have turned and they could have recouped all their positions. They would have incurred loss in the short-term but in the long-term they would have been fine.

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Some really inane comments in here. Obviously if you get unlimited liquidity, you can survive anything. That's not the point though. You can extend that argument and say that compounding 4% over 2000 years will give you more money than currently exists in the world today. If only you had enough liquidity and time...

Monkey, you're basically challenging people to predict the future. That's not possible. Things will always be mispriced at times if there exist unpredictable events. Black swans, by definition, are unpredictable. Though that doesn't mean what happened in 2008-2009 was a black swan. And a lot of newer options pricing models that traders/quants actually use do incorporate fat-tailedness.

If options were priced correctly, there would have been a lot less willing buyers of the options LTCM was selling and their profit potential would have been reduced. The same is true for the mortgage junk that was sold. But it's actually a good business proposition. If you had a 1 in 100 chance of losing other people's money and a 99 in 100 chance of sharing in the profits, wouldn't you take it too? That's the problem with regulations in finance.

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1, LTCM's main strategy was not using Black Scholes to make money, it was between off the run and on the run bonds and minute price differences like that. They were basically leveraged to the max exploiting small price differences. The problem was that the spreads they were betting on exploded during the black swan event (Russia) and they couldnt meet margin.

Black Scholes already has a way of incorporating black swans, its called the vol surface and the fact that implied vol trades historically above realized vol.

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By the way, I want to challenge the academic in the first video who claims that winning in the market is simply a matter of luck. Many, many academics economists and finance professors believe this (it seems to be the dominant view in the profession). Many of them even claim to have "proven" it. Their proof relies on the fact that beating the market one year, is not a good predictor of beating the market the next year. However, their studies overlook the simple fact that skill is not the same thing as return. If I run a $1B mutual fund and earn a 10% return, that demonstrates a lot more skill than someone earning a 10% return investing $1000 their own money. These studies overlook the fact that if you have skill, you might not get a higher return than the next guy, but rather an equal return with infinitely more capital.

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By the way, I want to challenge the academic in the first video who claims that winning in the market is simply a matter of luck. Many, many academics economists and finance professors believe this (it seems to be the dominant view in the profession). Many of them even claim to have "proven" it. Their proof relies on the fact that beating the market one year, is not a good predictor of beating the market the next year. However, their studies overlook the simple fact that skill is not the same thing as return. If I run a $1B mutual fund and earn a 10% return, that demonstrates a lot more skill than someone earning a 10% return investing $1000 their own money. These studies overlook the fact that if you have skill, you might not get a higher return than the next guy, but rather an equal return with infinitely more capital.

I don't think the amount of capital invested is any way to evaluate skill. I understand that in practice managing $1B is no the same as $1K, but there are many portfolio managers who run smaller funds but are much more successful than some of the big boys. The size of your portfolio often is a function of your returns in recent years, which could certainly be attributable to luck. The most skilled portfolio manager would provide solid returns with the lowest amount of risk. How you measure that risk, as has been pointed out in this thread, is the billion dollar question. This is why it's so hard to pick out the "best" managers, because at present I don't think that any quantitative metrics (returns, volatility, size of portfolio) are sufficient.

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I don't think the amount of capital invested is any way to evaluate skill. I understand that in practice managing $1B is no the same as $1K, but there are many portfolio managers who run smaller funds but are much more successful than some of the big boys. The size of your portfolio often is a function of your returns in recent years, which could certainly be attributable to luck. The most skilled portfolio manager would provide solid returns with the lowest amount of risk. How you measure that risk, as has been pointed out in this thread, is the billion dollar question. This is why it's so hard to pick out the "best" managers, because at present I don't think that any quantitative metrics (returns, volatility, size of portfolio) are sufficient.

You clearly do not know anything about liquidity then.

And Econ wasn't saying that size of the portfolio is what determines skill, but returns adjusted by amount you are managing.

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I don't think anything I said would imply that. In fact, I acknowledged that manging a $1B portofolio is not the same as a $1K argument. All I disagreed with that given equal average returns, I would not use size as the metric to pick one manager or the other.

And Econ wasn't saying that size of the portfolio is what determines skill, but returns adjusted by amount you are managing.

I understand and agree with that. I'm not saying size shouldn't be considered (and I know he wasn't saying that it's the only thing to consider) but I would rank risk as a bigger factored than size. Measuring the risk is obviously the hard part.

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All I disagreed with that given equal average returns, I would not use size as the metric to pick one manager or the other.

By the way, I wasn't saying you should pick the bigger manager to invest with. I'm saying he's arguably more skillful, even though people should be indifferent between investing in the two, because (at the margin) they're both going to give you equal returns. Again, my point is that defining skill in a quantifiable way is difficult, so maybe most academic studies that try to prove there's no skill in successful traders/investors completely miss the boat.

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All I disagreed with that given equal average returns, I would not use size as the metric to pick one manager or the other.

By the way, I wasn't saying you should pick the bigger manager to invest with. I'm saying he's arguably more skillful, even though people should be indifferent between investing in the two, because at the margin, they're both going to give you equal returns.

I understand and agree. Basically all I was saying is that if you are going to rank factors that demonstrate skill of a fund manager, I would put 1) Average returns, 2) Risk (however you can best measure it) and then 3) Size of portfolio managed.

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I don't think the amount of capital invested is any way to evaluate skill.

Sorry, I didn't mean to make it sound like size and skill are the same thing. All I meant, was that skill itself is complex and not easy to define. Academics often look solely at returns and I'm arguing that it's a mistake to do so, since just by adding size into the mix, you can easily see that returns are (at least in some cases) not the best proxy. I'm sure we can find even more variables to add to the mix, which will make skill even more complicated to quantify. And, if you can't quantify skill, you can't test whether some investors or traders are skillful. That's why academics try to define skill in a way that is tractable and quantifiable, but they might lose the essence of what skill really is, and therefore not even be able to test it.

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The most skilled portfolio manager would provide solid returns with the lowest amount of risk. How you measure that risk, as has been pointed out in this thread, is the billion dollar question. This is why it's so hard to pick out the "best" managers, because at present I don't think that any quantitative metrics (returns, volatility, size of portfolio) are sufficient.

I totally agree. The problem for academics, is that they cannot measure this sort of thing. So, they say, "it's not scientific" and then just stick with their quantifiable but inaccurate definitions of "skill" and call that science. More proof, that economics and finance are not sciences, and never will be...

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In video 3, they say something about them reducing everything to "measurable" quantities. Is this even true? They have volatility in there, I think what they really want is anticipated volatility or something. Sure, they have the backwards looking volatility of a stock, but that's not necessarily what's pricing options, since presumably traders and investors care about the future volatility of a stock. Right?

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I've always thought that Tiger Cubs were the main argument against the EMH

If I had asked people what they wanted, they would have said faster horses - Henry Ford

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I think one of the biggest mistakes in modern finance is the belief that volatility = risk. Volatility is just a measure of how much something moves around. Risk, at least to me, is more about max drawdowns. Sharpe ratios are an imperfect method to reconciliate this difference between volatility and expected return, but it leaves out fat tail events and has other failings. You can use options to hedge your positions and limit your downside. Thus, you can have really high volatility, capture those returns, but at the same time insure against fat tail events. That, to me, is the best way to trade, long-term fundamentals-based bets, with high volatility (no other way to get truly high returns), but insuring against fat tail events such that you are minimizing your drawdowns.

LTCM was actually making a huge directional bet, they just didn't realize that's what they were doing. That plus not insuring against fat tail movements against that directional bet (not to mention insane leverage ratios) took them out.

I recommend "When Genius Failed", one of the best investing books ever, lots of great lessons in there...

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I think one of the biggest mistakes in modern finance is the belief that volatility = risk. Volatility is just a measure of how much something moves around.

Am I misinformed, because I thought most people know that volatility is not a good measure of risk? If one can diversify some of that volatility away (through other financial instruments) then it's not as risky as volatility suggests. I guess I'm thinking of the covariance with other instruments or an entire portfolio...

alexpasch:

I recommend "When Genius Failed", one of the best investing books ever, lots of great lessons in there...

Can someone write a post about this book? I'm really curious to hear some of the main lessons that you guys drew from it.

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If I had asked people what they wanted, they would have said faster horses - Henry Ford

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Besides, I like economizing on time. That's why I like EconTalk podcasts so much -- I can often get the essence of a book in just one hour. I tried looking on youtube for the author discussing the book, but no such luck.

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I just don't get any Black-Scholes or similar model - don't they all rely on probability (standard deviation or any more fancy sd related stuff, which is still sd in essence), and given they all rely on probability, how can you calculate probability of events that do not have a fixed number of outcomes? Because of this essential feature, all BS just mean BS to me, like what BS means in everyday usage. If LTCM "worked" for a while, it was because they were heavily leveraged and lucky - which just multiplied the returns they would get on normal "up" market, hence all the beating the market crap... Black Swans will happen, if not in one form, then in another, the markets will change... how can you take historical data as some kind of proof of future?

Dynamically measuring far tail likelihood, and then automatically calling all stops on standard models (like Var and B-S) once economy goes into uncharted waters is an interesting idea... But then if you leave that exit option open, you can't really price options anymore, at least mathematically.... All options writers will start including legal terms which would make contracts valid only under "normal" economic conditions, aka guaranteed returns*

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I just don't get any Black-Scholes or similar model - don't they all rely on probability (standard deviation or any more fancy sd related stuff, which is still sd in essence), and given they all rely on probability, how can you calculate probability of events that do not have a fixed number of outcomes? Because of this essential feature, all BS just mean BS to me, like what BS means in everyday usage. If LTCM "worked" for a while, it was because they were heavily leveraged and lucky - which just multiplied the returns they would get on normal "up" market, hence all the beating the market crap... Black Swans will happen, if not in one form, then in another, the markets will change... how can you take historical data as some kind of proof of future?

I think many would agree with you in terms of the limitations of B-S, but have you read When Genius Failed? It strikes me that you think they beat the market by speculating on equity options, which is simply false. Their returns had nothing to do with whether the markets was up or down, but rather the inefficiencies in fixed income markets. They used their models to effectively find pricing disparities between markets. One example that someone already pointed out was "off-the-run" Treasuries pricing inconsistently with new issues.

The problem they ran into is that even when they were doing well, they were making money of tiny spreads by using leverage. As time went on, and the markets became relatively more efficient, they had to use more leverage to generate the same returns. They were essentially picking up pennies in front of a bulldozer. The assumption that killed LTCM was that they could stay solvent longer than the markets could stay inefficient.

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I think many would agree with you in terms of the limitations of B-S, but have you read When Genius Failed? It strikes me that you think they beat the market by speculating on equity options, which is simply false. Their returns had nothing to do with whether the markets was up or down, but rather the inefficiencies in fixed income markets. They used their models to effectively find pricing disparities between markets. One example that someone already pointed out was "off-the-run" Treasuries pricing inconsistently with new issues.

The problem they ran into is that even when they were doing well, they were making money of tiny spreads by using leverage. As time went on, and the markets became relatively more efficient, they had to use more leverage to generate the same returns. They were essentially picking up pennies in front of a bulldozer. The assumption that killed LTCM was that they could stay solvent longer than the markets could stay inefficient.

Thanks for clarification, I agree, I went a little too far with the LTCM example - they weren't really trading stocks or things deriving value from stocks, to my knowledge, so the connection with "market" is a little bit far fetched. But the whole principle of taking a probability of an event without fixed number of outcomes still holds true. You cannot ignore these far tails, since the losses during these couple of years can outweigh small consistent gains over stable years. Its like playing roulette (from casino perspective), the chances of player hitting a number are lower than those of hitting odd/even, but the payout is far greater. If somebody bets large, and starts hitting numbers, you can quickly be out of business. Good thing with roulette you can calculate exact odds, knowing exactly both the likelihood of an event and the exact payout during it (of course, wheels can be faulty, etc., but thats mechanical problems). In markets you can't really do that - you can only say based on the last 20-30 years - this is the risk I get. But whats the guarantee next 20-30 years will be like those before. Many things change, e.g. people started to save money in pension funds which surely drew stock prices up, and that had nothing to do with company financials getting better... does it has to continue? no! Alternatively, does it mean taking model with 50 year year span will provide too conservative estimates, since market is different now, everybody expects more risk/return? But what happens when demography changes and there are less people putting moneys into pensions funds, than withdrawing them? This is the problem I have with models. They tend to ignore different "scenario" factor, pr model it exceptionally loosely, since what you haven't yet observed is very hard to quantify (no data to build equations).

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In markets you can't really do that - you can only say based on the last 20-30 years - this is the risk I get. But whats the guarantee next 20-30 years will be like those before. Many things change...

I totally agree. That's a big problem with many formal models in finance and econ. I think researchers in these disciplines make an assumption (wishful thinking?) that the numbers will stay "relatively" constant. As F.A. Hayek and some other economists have pointed out, there are probably no empirical constants in social sciences.

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I just don't get any Black-Scholes or similar model - don't they all rely on probability (standard deviation or any more fancy sd related stuff, which is still sd in essence), and given they all rely on probability, how can you calculate probability of events that do not have a fixed number of outcomes? Because of this essential feature, all BS just mean BS to me, like what BS means in everyday usage. If LTCM "worked" for a while, it was because they were heavily leveraged and lucky - which just multiplied the returns they would get on normal "up" market, hence all the beating the market crap... Black Swans will happen, if not in one form, then in another, the markets will change... how can you take historical data as some kind of proof of future?

Dynamically measuring far tail likelihood, and then automatically calling all stops on standard models (like Var and B-S) once economy goes into uncharted waters is an interesting idea... But then if you leave that exit option open, you can't really price options anymore, at least mathematically.... All options writers will start including legal terms which would make contracts valid only under "normal" economic conditions, aka guaranteed returns*

*- unless markets go down

watch the video i posted earlier.

I think people are gettting their nipples overly twisted with the assumptions of B-S.

The key usage of BS is to find the implied volatilities from option prices. Option prices themselves are determined by supply and demand in the market place, and since you are trading volatility you need to know the price of options in vol terms.

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I just don't get any Black-Scholes or similar model - don't they all rely on probability (standard deviation or any more fancy sd related stuff, which is still sd in essence), and given they all rely on probability, how can you calculate probability of events that do not have a fixed number of outcomes?

You're kidding right? You use the cumulative density function to get the probability. While the B-S has it's limitations, it's incredibly useful. From your post, I find it hilarious that you seem to know nothing about B-S but at the same time deem it BS. Just because you don't understand it doesn't make it wrong.

Consultant to a Fortune 50 Company

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I just don't get any Black-Scholes or similar model - don't they all rely on probability (standard deviation or any more fancy sd related stuff, which is still sd in essence), and given they all rely on probability, how can you calculate probability of events that do not have a fixed number of outcomes?

You're kidding right? You use the cumulative density function to get the probability. While the B-S has it's limitations, it's incredibly useful. From your post, I find it hilarious that you seem to know nothing about B-S but at the same time deem it BS. Just because you don't understand it doesn't make it wrong.

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I just don't get any Black-Scholes or similar model - don't they all rely on probability (standard deviation or any more fancy sd related stuff, which is still sd in essence), and given they all rely on probability, how can you calculate probability of events that do not have a fixed number of outcomes?

You're kidding right? You use the cumulative density function to get the probability. While the B-S has it's limitations, it's incredibly useful. From your post, I find it hilarious that you seem to know nothing about B-S but at the same time deem it BS. Just because you don't understand it doesn't make it wrong.

Explain to me how you can price the option of a particular stock using the cumulative density function and NOT using the stock's or other linked variable's historic volatility...

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